∫ x sin ( x 2 ) d x {\displaystyle \int x\sin {(x^{2})}dx}
u = x 2 d u = 2 x d x 1 2 d u = d x {\displaystyle {\begin{aligned}u&=x^{2}\\[2ex]du&=2xdx\\[2ex]{\frac {1}{2}}du&=dx\\[2ex]\end{aligned}}}
∫ x sin ( x 2 ) d x = 1 2 ∫ sin ( u ) d u = − 1 2 cos ( u ) + C = − 1 2 cos ( x 2 ) + C {\displaystyle {\begin{aligned}\int x\sin {(x^{2})}dx&={\frac {1}{2}}\int \sin {(u)}du\\[2ex]&=-{\frac {1}{2}}\cos {(u)}+C\\[2ex]&=-{\frac {1}{2}}\cos {(x^{2})}+C\end{aligned}}}
![{\displaystyle {\begin{aligned}u&=x^{2}\\[2ex]du&=2xdx\\[2ex]{\frac {1}{2}}du&=dx\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/d3662e4ad2b3d50be2a69669e39b54ac46042ca4)
![{\displaystyle {\begin{aligned}\int x\sin {(x^{2})}dx&={\frac {1}{2}}\int \sin {(u)}du\\[2ex]&=-{\frac {1}{2}}\cos {(u)}+C\\[2ex]&=-{\frac {1}{2}}\cos {(x^{2})}+C\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/ee0244989664f2dd175ffcbffed3ada5167b3cf6)